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In this study, we solve by involving conformable fractional derivative on time-fractional perturbed nonlinear Schrödinger model which describe the behaviour of soliton transmission on fibers optical system in physics specially in transmission of data over long distances with large bandwidth. There are two modern techniques are utilized for solving the suggested model namely the Extended hyperbolic function technique and the polynomial expansion technique. These techniques give unique, robust, and powerful solutions that are useful in many research areas. We attain different types of solutions that give unique behaviour of V shaped, singular solution, and periodic soliton solutions. These solutions are play a vital role in the soliton theory along with data transmission in optical fibers. Further we also discuss the stability of obtain solutions as well as the modulation instability of the governing NLSE. To grasp and better understanding of the solution behavior we include the 3D, contour and 2D graphics. [ABSTRACT FROM AUTHOR]

The generalized Korteweg–de Vries–Zakharov–Kuznetsov model is one of the dominant nonlinear complex structures to exhibit the influence of magnetic fields on weak ion‐acoustic waves in plasma made up of cool and hot electrons. In this study, the nonlinear higher dimensional model is subjected to the extended F$$ F $$‐expansion approach and the exp(−ϕ(ζ))$$ \exp \left(-\phi \left(\zeta \right)\right) $$‐expansion strategy in order to discover some novel traveling waves solutions and other exact solutions. There have been several solutions discovered, such as bright, dark, periodic, bell‐shaped, and single bell‐shaped wave structures. Furthermore, the stability analysis of the model is also reported along with the dynamical visualization of the charismatic behavior of various solitons with the aid of 3D, 2D, and contour plots. The proposed techniques can also be implemented to analyze a wide range of nonlinear evolution models emerging in diverse disciplines of science and technology including mathematical physics and plasma physics. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation is one of the significant nonlinear complex models describing the optical solitons in dispersive media. In this study, the (2+1)-dimensional chiral nonlinear Schrödinger model has been investigated analytically which is of key importantance in the field of fluid sciences. A variety of exclusive travelling waveform solutions have been established for the complex dynamical model by employing a set of eminent analytical approaches namely the extended modified auxiliary equation mapping method, the improved F -expansion method, and the unified method, respectively. We obtained different forms of solitary types solutions with the help of these technique. The outcomes are a set of bell-shaped, single periodic, optical, and multi-periodic solutions. Finally, the stability of the developed results is also established to validate the computations. The study provides a very spectacular and appropriate way to put together several interesting wave demonstrations for more complex models of current era. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear dispersive structure namely the modified Benjamin–Bona–Mahony (BBM) model is studied by employing three different approaches to develop some new analytical and semi-analytical solutions. The modified extended t a n hyperbolic function method, the improved F -expansion method and the Adomian decomposition method are implemented to obtain various interesting wave structures. The comparison among various types of solutions is analyzed to study the corresponding absolute error. Furthermore, the stability of the results along with the modulation instability are successfully deliberated. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behavior. [ABSTRACT FROM AUTHOR]

In this study, the (2+1)-dimensional generalized Hirota–Satsuma–Ito model is studied extensively to investigate wave dynamics of shallow water. A set of state of the art analytical approaches are being employed to acquire several fascinating wave structures. We have established a comparison between exact and numerical solutions to determine the absolute error. Moreover, the modulation instability as well as the stability of the solutions are adequately discussed. The 3D, contour and 2D plots are displayed for several interesting exact solutions to understand their behaviour. These strategies are demonstrated as more strong, effective, and efficient in developing various new wave structures which have numerous applications in several mathematical physics domains. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is one of the most important physical models for explaining the dynamics of optical soliton proliferation in optical fibre theory. Due to an extensive variety of applications for ultrafast signal routing systems and short light pulses in communications, optical soliton propagation in nonlinear fibres is a topic of substantial present interest. To overcome the ill-posedness of the unstable NLSE, a new term L x t is introduced which leads to the Hamiltonian amplitude equation. In this work, we study exact wave solutions to the nonlinear complex model by utilizing a set of analytical approaches namely as the exp (− ξ (δ)) method, the improved F-expansion technique, and the extended modified auxiliary equation mapping method. Numerous solutions, including singular periodic, multi-periodic, single bell-shaped, and multi-bell-shaped wave frameworks were found. The proposed plan of action is swift, strong, as well as offers the requirements needed to verify the origin of these solutions. Additionally, a dynamics representation of the fascinating behaviour of several solidarity using 2D, 3D, and contour graphs is provided, also we discuss the stability analysis and modulation instability of the proposed model. [ABSTRACT FROM AUTHOR]